If Paul allowed a divorce in the case of an unbeliever abandoning a believer, could a divorce also apply for a believer abandoning a believer?
No, because Paul would expect a believing husband or wife to follow the Church's guidance on how they should behave, and reconcile. There's the famous example of the man who told his pastor "I don't love my wife anymore" and received the reply "The Bible tells us to love our wife (Ephesians 5:25,28), to love our neighbour (Matthew 22:39), and to love our enemy (Luke 6:27), and at least one of those applies here."
Of course, if someone abandons their husband/wife and does
not listen to the Church, then they are effectively abandoning the Church as well, and have to be considered as an unbeliever (i.e. they would be excommunicated).
If the abandonment involves an affair, Matthew 19:9 applies (
I tell you that anyone who divorces his wife, except for marital unfaithfulness, and marries another woman commits adultery).
As to abuse, I would interpret that as abandoning the marriage vows (1 Corinthians 7:15:
But if the unbeliever leaves, let him do so. A believing man or woman is not bound in such circumstances; God has called us to live in peace). Some people call this "constructive desertion," and view it as part of the "flip side" of Matthew 19:9.
The other relevant passage for abuse is 1 Peter 3:7 (
Husbands, in the same way be considerate as you live with your wives, and treat them with respect as the weaker partner and as heirs with you of the gracious gift of life, so that nothing will hinder your prayers), which refers of course to the fact that women are generally
physically weaker (Greek ἀσθενεστέρῳ
than their husbands. And of course, husbands are told in the Bible to love their wives as Christ loved the Church (Ephesians 5:25). An abusive husband (on top of everything else) shows a contempt for Christ that's difficult to reconcile with true belief.